Simplify the following expression: $ z = \dfrac{1}{3} - \dfrac{-2k}{-3k - 3} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-3k - 3}{-3k - 3}$ $ \dfrac{1}{3} \times \dfrac{-3k - 3}{-3k - 3} = \dfrac{-3k - 3}{-9k - 9} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{-2k}{-3k - 3} \times \dfrac{3}{3} = \dfrac{-6k}{-9k - 9} $ Therefore $ z = \dfrac{-3k - 3}{-9k - 9} - \dfrac{-6k}{-9k - 9} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{-3k - 3 + 6k }{-9k - 9} $ Distribute the negative sign: $z = \dfrac{-3k - 3 + 6k}{-9k - 9}$ $z = \dfrac{3k - 3}{-9k - 9}$ Simplify the expression by dividing the numerator and denominator by -3: $z = \dfrac{-k + 1}{3k + 3}$